The math:
Pj Problem of Interest is of type force (pull). Modulus of resilience is strain energy absorbed per unit volume. Energy and Work problems are in general force problems. In this case the force is tension force (pull).

Formulas of interest:
Modulus of resilience ur, is strain energy absorbed per unit volume.
ur = Pδ/2V = σplεpl/2 ---------(1)
Where P is load at the proportional limit. Proportional limit is the maximum stress a material can sustain without deviating from the law of stress-strain proportionality.
δ is elongation due to P
V is volume
σpl is stress at proportional limit
εpl is strain due to σpl